SOLUTION: Can I please ask for help as I need to write 2loga x+1/3loga y-loga z as a single logarithm. Thank you so much.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can I please ask for help as I need to write 2loga x+1/3loga y-loga z as a single logarithm. Thank you so much.      Log On


   

Question 811759: Can I please ask for help as I need to write 2loga x+1/3loga y-loga z as a single logarithm. Thank you so much.
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
2log%28a%2Cx%29+%2B+%281%2F3%29log%28a%2Cy%29+-+log%28a%2Cz%29
these logs all have the same base so we can go straight into combining them.
before we do this, we need to take the numbers before the log and make them into exponents alogb=logb%5Ea
log%28a%2Cx%5E2%29+%2B+log%28a%2Cy%5E%281%2F3%29%29+-+log%28a%2Cz%29
now use the multiplication and division properties.
loga%2Blogb=logab
loga-logb=%28loga%29%2F%28logb%29
log%28a%2C%28x%5E2y%5E%281%2F3%29%29%2Fz%29
log%28a%2C%28x%5E2%2Aroot%283%2Cy%29%29%2Fz%29